if cos(pi/4) is sqrt2/2
i thought sec(pi/4) is 2/sqrt 2,but its just sqrt 2 . can some one please explain.
remember that cos pi/4 can also be expressed 1/sqrt2. so 1/1/sqrt2=sqrt2.
To understand why sec(pi/4) is equal to sqrt(2), we need to start by understanding what the secant function represents.
The secant function (sec) is defined as the reciprocal of the cosine function (cos). Mathematically, sec(x) = 1/cos(x).
Now, let's calculate sec(pi/4).
We know that cos(pi/4) is sqrt(2)/2 based on the given information. So, we can substitute this value into the formula: sec(pi/4) = 1/cos(pi/4).
Replacing cos(pi/4) with sqrt(2)/2, we have: sec(pi/4) = 1/(sqrt(2)/2).
To divide by a fraction, we can multiply by its reciprocal. In this case, the reciprocal of sqrt(2)/2 is 2/sqrt(2), which gives us: sec(pi/4) = (1 * 2)/(sqrt(2)/2).
Now, we can simplify this expression: sec(pi/4) = (2)/(sqrt(2)/2).
To divide by a fraction, we can multiply by its reciprocal. The reciprocal of sqrt(2)/2 is 2/sqrt(2), giving us: sec(pi/4) = (2)/(sqrt(2)/2) * (2/sqrt(2)).
Multiplying the numerators and denominators, we get: sec(pi/4) = 4/(sqrt(2) * sqrt(2)).
sqrt(2) * sqrt(2) can be simplified to 2. So, we have: sec(pi/4) = 4/2.
And simplifying further, we get: sec(pi/4) = 2.
Therefore, sec(pi/4) is indeed equal to sqrt(2).